Mayor Giuliani yesterday remained tantalizingly silent on when he’ll throw his hat into the Senate ring — saying Hillary Rodham Clinton’s decision to run won’t put pressure on his political timetable.

Asked by reporters when he might announce his own candidacy in the wake of Clinton’s declaration Tuesday, Giuliani said, “When I’m ready.

“I’ll answer it on my own time and in my own way, and I’m not going to let outside events force me into a decision. … So far, our strategy is working, so there’s no reason to change it.”

Speaking at City Hall, the mayor wouldn’t elaborate on his “strategy,” saying it’s “working better than we thought. I think you all know that, so I don’t have to emphasize it.”

The mayor has repeatedly said he is interested in running for the Senate and has held political fund-raisers across the country — often while invoking the first lady’s name.

Noting that the mayor never officially announced his re-election campaign in 1997, his advisers all privately say he is running.

With Tuesday’s announcement, Clinton has made it clear she’s in the race for keeps. Her campaign spokesman, Howard Wolfson, said Giuliani now should clearly state his intentions.

“Why won’t the mayor tell New Yorkers whether he’s running? Is he afraid to talk about all those national issues that he is trying to avoid?” Wolfson said.

The first lady will be back in New York on Monday, and will be the featured guest at a Manhattan fund-raiser for Queens Democratic Rep. Joe Crowley — something that has angered at least one local abortion-rights activist.

“We’re disappointed by this because Congressman Crowley is against a woman’s right to choose,” said Kelli Conlin, executive director of the local chapter of the National Abortion and Reproductive Rights Action League.

“He is one of our major targets next year and it could be a very competitive primary. We hope that the first lady will also attend a fund-raiser for any of Congressman Crowley’s opponents.”

Conlin noted that NARAL at times has also been angry with Giuliani, who — while pro-choice himself — has taken part in fund-raisers for anti-abortion Republicans.